I have seen and heard 4 or 5 deer do the snort wheeze.
All but 1 were big bucks.

The last one was either an immature buck or a medium sized doe that philbert8 and I scared out of a bed midday. He/She got up and ran about 20 yards then stopped, turned his/her head our way and snort/wheezed, stomped the ground, then split.

That could be the exception to the rule but I' d say that any deer could do it if they were willing.